(x-5)(x-13)=0

Solution for (x-5)(x-13)=0 equation:

(x-5)(x-13)=0

We multiply parentheses ..

(+x^2-13x-5x+65)=0

We get rid of parentheses

x^2-13x-5x+65=0

We add all the numbers together, and all the variables

x^2-18x+65=0

a = 1; b = -18; c = +65;
Δ = b2-4ac
Δ = -182-4·1·65
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-8}{2*1}=\frac{10}{2}
=5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+8}{2*1}=\frac{26}{2}
=13
$